Graph Valid Tree


Introduction

The objective is to write a function that returns true (or 1) if a given undirected graph is a tree and false (or 0) if it is not a tree. A graph can be classified as a tree if it satisfies the following two conditions: -

  • Each node, except the root node, must have a single parent. That is, each node must be reached only from its parent when the tree is being traversed starting from the root.
  • We must be able to visit all the nodes of the tree starting from the root. Therefore, a tree should always be connected, and all nodes must be reachable.

 

Problem Statement

Let us consider two graphs as shown in the figure below:

 



Figure 1 shows a valid tree as it has no cycles, and has n-1 edges for n nodes.

Figure 2 is invalid as it contains a cycle connecting 1 and 2.

A function is to be written that returns 1 if the given graph is a valid tree and 0 if it is not a valid tree.

(Check out the details for the problem of the graph valid tree)

 

PsuedoCode with Explanation

Suppose there are n nodes labelled 0 to n-1 and a list of undirected edges [u,v] showing a connecting path from u to v. We have to make a function to check whether the tree formed by the given edges is valid or not.

For example, if the input is n = 5, and edge = [[0,1], [0,2], [0,3], [3,4]], as show in figure 1, then the output will be true.

 

The following steps are taken to solve this: -

  • Define a function is_valid(), this will take node, par, graph, and another array called visited.
  • If visited[node] == 1, then return true


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